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Double Series and Convergence Tests

In: Convergence Methods for Double Sequences and Applications

Author

Listed:
  • M. Mursaleen

    (Aligarh Muslim University, Department of Mathematics)

  • S. A. Mohiuddine

    (King Abdulaziz University, Department of Mathematics)

Abstract

Since Pringsheim introduced the notion of convergence of a numerical double series in terms of the convergence of the double sequence of its rectangular partial sums. However, an exhaustive treatment giving analogues of all well-known convergence aspects of single series seems to be unavailable. In this chapter, we give results to fill in some of the gaps in such a treatment and also to point out some errors in previous attempts to obtain results exactly analogous to those of a single series.

Suggested Citation

  • M. Mursaleen & S. A. Mohiuddine, 2014. "Double Series and Convergence Tests," Springer Books, in: Convergence Methods for Double Sequences and Applications, edition 127, chapter 0, pages 149-166, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1611-7_9
    DOI: 10.1007/978-81-322-1611-7_9
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